The lions in Santiago's dreams are the ones that he observed as a young boy sailing on large ships. He remembers this time of his life as a pure pleasure, with no negative memories attached to it, and becomes happy whenever he dreams of the lions playing on the beach:

He no longer dreamed of storms, nor of women, nor of great occurrences, nor of great fish, nor fights, nor contests of strength, nor of his wife. He only dreamed of places now and of the lions on the beach. They played like young cats in the dusk and he loved them...(Hemingway, The Old Man and the Sea, Google Books)

One interesting comparison is the mention of Santiago's wife; she died, and he has removed her picture from his shelf because it makes him sad. Despite the many happy memories he must have of her, the sad memory of her death makes him shunt those memories aside, so he doesn't have to think of them. Because all the memories of the lions are good, he can dream of them and remember his youth when he had no fear, no guilt, and no sorrow.